PLAUSIBLE CONSIDERATIONS REGARDING THE ASTRONOMICAL ... · practice luni-solar calendars. b.1) The...

LLULL, vol. 17, 1994, 469-514

PLAUSIBLE CONSIDERATIONS REGARDING THEASTRONOMICAL MODELLING OF THE SOCIALAND BIOLOGICAL LIFE OF DACIANS-GETIANS

LIVIU SOFONEAPhysics DepartmentUniversity of Brasov

NICHOLAS IONESCU-PALLASRomanian Society for General Relativity and Gravitation

RESUMEN

En este artículo se presentanalgunas consideraciones.plausiblessobre la existencia de un calendarioespecialmente desarrollado en lacivilización y cultura de los Getas-Dacios, localizado en la (supuesta)capital Sarmisegetusa Regia/Basileia/Cogaionon. Se expone un modeloteórico plausible para un calendarioDacio-Geta hipotéticamente lumi-solar utilizado en la Antigiiedad enSarmisegetusa y se hacen tambiénalgunos comentarios epistemoló-gicos.

ABSTRACT

1n the paper is presented someplausible considerations regarding theexistence of a calendar speciallydeveloped within the civilization &culture of Getians-Dacians andlocated in the capital (presumed)Sarmisegetusa Regia/Basileia/Cogaionon. A plausible theoreticalmodel of a hypothetic lunisolarDacian-Getian calendar used inAntiquity in Sarmisegetusa isworked. Some epistemologicalcomments are also made.

Palabras clave: Calendarios, Cronologías, Astronomía, Antigtiedad.

1. Plausible • considerations regarding the existence of acalendar specially developed within the civilization and cultureof Getians-Dacians

In memorian professor Ilie Preda Mosic (1911-1993)

The remarkable civilization and culture I created on the Carpanthian-Danubian-Pontic territory by Dacians-Getians plausibly, even necessarily,

Recibido el 15 de mayo de 1994

470 LIVIU SOFONEA Y NICHOLAS IONESCU-PALLAS

LLULL 17

implies the existence of a well-defined system for the time-reckoning, used fororganizing both the social-cultural life and the individual one.

Establishing some correspondences between the rhythms of biologicallife and the astronomical and climatic periods, marked by the periodic motionsof sun and moon, is, certainly, a natural and longstanding process to be foundto all the peoples founders of ancient civilizations and cultures in the giantarea from Indus to Atlantic Ocean 2, area inhabited in Antiquity. We have noargument to believe that Dacians-Getians were, in this respect, an exception.

Contrarily:

a) The healthy climate of the Dacia's regions, the mineral and vegetalriches, the active social life, the serenity of the Dacian soul, as it wasmentioned in different historical testimonials, their bending towards wisdomand towards the cultivation of liberal arts as well, as the resorting to a richpharmacopoeia -all these arguments, and others, naturally guide us to concludeupon the existence to Dacians-Getians of many cases of impressivelongevity3.

b) The intense economical and cultural exchanges between Dacia and thelands of the Mediterranean Basin, and of the Near East, advocate4 for theexistence of a luni-solar caleridar, with the subsequent divisions: days, decades,months, years, and (plausible) still longer periods5 , because, both Greeks andRomans -obviously the most important partners of Dacians-Getians in theireconomic and cultural dialogue with foreign countries- still had in theirpractice luni-solar calendars.

b.1) The Greek calendar was based on the Meton's cycle T 19 solaryears, and was considered as the most accurate system of time-reckoning atthat epoch6.

b.2) The Roman Calendar already underwent some significant changing,i.e. in the early Republican epoch was used (probably) a luni-solar calendarbased on a eight years cycle7 , and before the year 46 BC8 a calendar(presumably) based on the T 11 years cycle and having years of variableduration9 according to the formulam:

355 x + 378 y + 377 z 4016x + y + Z = 11

X= 6,y= 1,z=4

The Roman cycle accurately included an integer number of lunar synodicperiods, namely N = 136.

LLULL 17 ASTRONOM1CAL MODELLING OF THE LIFE OF DACIANS-GETIAN S 471

The detailed arguments gathered by us to support the hypothesis of theexistence of a luni-solar calendar in Ancient Dacia-Getia, as well as our ownefforts to concretize it, are presented in the sequel.

In this respect a study of the elements with presumptive astronomicalmeaning of the great circular sanctuary from Sarmisegetusa, the royal capitalof the Dacia-Getia prior to Roman conquest 11 is undertaken in view ofachieving a reconstruction of the Dacian-Getian calendar:

a) accounting, more plausible, for the ancient traditions of timereckoning;

b) accounting more plausible, for the cultural influences exerted uponDacian-Getian territory.

More definitely, the following logical and archaeological-historicalarguments are taken into consideration:

a) Zamolxes, the founder of Dacian-Getian religion studied astronomy12in Egypt, in Ancient Israel and Chaldea13.

b) Deceneu, the great priest of the Dacian-Getian monotheist religionduring the reign of the king Buerebista, studied 14 astronomy from Greeks andJews15.

c) The strange tablets with cuneiform inscriptions found in Tartaria onthe Mures river exhibit 16 a significant analogy with similar tablets ofSumerian origin 17 , or wich Cretan tablets18.

d) The hypothesis, according to which in the last half of the thirdmillennium B.C. a definite and intensive trade transit coming from Indusgoing through Mesopotamia and Syria up to Danube, was put forward 19 . Ifthis hypothesis, supported by palaeographic proofs, will turn out to be a validand important one, then the Oriental influence upon Dacia-Getia appears notonly as likely, but still having an impressive tradition.

e) It was established some connecting lines between the megalithiccivilizations of France and England and the civilizations of the Far East20(India and Mesopotamia). One if these lines joined Troy of Priam toStonehenge, via the Vinca culture, located on the Dacian territory21.

f) The study of the constructions with a presumed astronomicaldestination, both from Stonehenge and Sarmisegetusa 22 , revealed a series ofstriking analogies which by no means may be overlooked23.

472 LIVIU SOFONEA Y NICHOLAS IONESCU-PALLAS LLULL 17

g) Some historical sources, dated towards the end of Roman Antiquity,mention the existence of some relevant Cultural including scientific24exchanges25 between Dacians-Getians and Celts26.

h) Some various investigations 27 proved, in a convincing way, that themegalithic building of Stonehenge was proper to be operated as an eclipsepredictor, because in the construction of the respective monument would beincluded the number of years of the cycle of lunar orbit nodes as a fraction N =56/3.

Starting from these arguments and frames -i.e. logic, archaeological-historical arguments- we were able to devise a model of the (presumed) Daciancalendar, giving, finally, its (plausible) delineation: it was (plausible) a luni-solar calendar, mainly based on the 11 years cycle for equalize an integernumber of synodic lunar periods with an integer number of sideral terrestrialperiods.

a) The keynote of our construction is the idea that: the circle made up ofN = 30 large stone pillars of the great circular sanctuary may have a doublefunction:

a.1) in a given rotational sense it is possible to reckon days;a.2) in the opposite sense it is possible to take into evidence the lunar

months.

b) Other details refer to:

b. 1) the division of a day and a month in sub-intervals;b.2) the system of corrections necessary to improve the correspondence

between the solar and the lunar parts of the calendar.

For all these aspects we were in a position to find out a motivation justin the numerology of Sarmisegetusa: i.e. the set of integer numbers deliveredby the finite and discrete number of the sanctuary elements.

a) We consider the large stone pillars28 as determining the structure of the(plausible) Dacian-Getian calendar 29 , from Sarmisegetusa: this is a basicarchaeological-numerological hipothesis of our (plausible) astronomical modelof the hypothetic Dacian-Getian calendar from Sarmisegetusa.

b) The motion of the Moon 30, has (presumably) a basic role and functionin the (plausible) Dacian-Getian calendar from Sarmisegetusa: this is the basicastronomical hypothesis of our (plausible) astronomical model of the(hypothetic) Dacian-Getian calendar from Sarmisegetusa31.

LLULL 17 ASTRONOMICAL MODELLING OF THE LIFE OF DACIANS-GETIANS 473

Our approach is a talcing over of the lunar hypothesis based both on:

b.1) the proofs meanwhile accumulated;and

b.2) the critical and correlative analysis of this amount of data.

c) There are many archaeological facts -observed, and stressed, from aparallel study of the old •monuments of Stonehenge and those similar ofSarmisegetusa- which, with the force of evidence, suggest an interesting (or,even, a relevant) analogy 32 . This (undeniable) analogy33 is used as aperemptory basis 34 for our own (plausible) reconstruction of the (hypothetic)Dacian-Getian calendar from Sannisegetusa.

The elements of the analogy are the following:

c.1) In both cases we come across a certain enclosure: occupying a centralplace, and having the shape of a horseshoe.

c.2) In both cases there is a great circle made up of N = 30 stoneelements: pillars at Sannisegetusa and great vertical blocks at Stonehenge.

c.3) In both cases it may be ascertained the existence of an intermediarycircle between the circle of N = 30 stone elements and the central horseshoeenclosure.

c.4) In both cases the great circular sanctuary was put in communicationwith a smaller construction: the small circular sanctuary at Sarmisegetusa andthe, so-called, Heel-stone at Stonehenge35.

c.5) In both cases the line joining the centre of the great sanctuary to thecentre of the smaller construction has the same (or a similar) meaning -that ofa geographical orientation36.

d) The motion of the Sun has (certainly) a basic role and function in the(plausible) Dacian-Getian calendar from Sarrnisegetusa.

d.1) A great success of the solar variant of the (plausible) Dacian-Getiancalendar was considered to be the possibility of incorporating the number N =34 in the structure of the respective calendar: because this number is just thenumber of wooden pillars of which is built up the horseshoe enclosure find inthe excavations of Sarmisegetusa.

d.1.1) The Romanian historian Constantin Daicoviciu proceeded to thedeciphering of the hypothesized Dacian-Getian calendar in a quite simple way:he conjectured that the Dacian-Getian year had T = 360 days;


d.1.2) The number of wooden pillars to be found on the N = 30 stonepillars circle (which is just N = 180) labelled a Dacian semester.

d.2) A necessary, and valuable, amendment was brought by a Frenchresearch worker, Georges Charriére, who observed as is mentioned in[DAICOVICIU, 1981, vol. 1. p. 254-255] that

d.2.1) If at every T = 34 Dacian years we add a Dacian semester then theaverage tropic year has T = (365 + 5/17) days. This result was considered assatisfactory: taking into account the general level of scientific knowledgereached by Dacins-Getians37.

d.2.2) As the number of wooden pillars making up the intermediary circle(placed between the N = 30 stone pillars ring and the horseshoe enclosure) isjust N = 68, i.e. the number of Dacian semesters entering the correctionperiod of T = 34 Dacian years, one was claimed to have in hand theexplanation for almost the whole numerology of the Great Temple ofSarmisegetusa.

d.2.2.1) N = 6 i.e. the number of wooden pillars placed between twoconsecutive stone pillars of the great circle made up of N = 30 stone pillars, isthe Dacian week.

d.2.2.2.) N = 30, i.e. the number of stone pillars making up the greatring of the sanctuary, is the Dacian month.

d.2.2.3) N = 180, i.e. the number of wooden pillars placed on the greatring, is the Dacian semester38.

d.2.2.4) N = 34, i.e. the number of wooden pillars of the horseshoeenclosure, is the number of Dacian-Getian years after which a correctiveDacian-Getian semester is added.

d.2.2.5) N = 68, i.e. the number of Dacian semesters entering acorrection period of 34 Dacian years.

d.3) An improved version of this scheme was put forward by DinuAntonescu, who suggested:

d.3.1) To add a corrective month at every T = 68 months rather than towait T = 34 years for adding an entire semester. In this way the climaticcorrespondence of the calendar is restored, but the (famous) horseshoe


enclosure is destitute of its presumed outstanding role, in favour of theintermediary circle (made up of N = 68 elements).

d.3.2) To make this suggestion operational we would be, naturally,guided to adopt a scheme based on a T = 17 years period made up of T = 3long years (of T = 13 months i.e. 13 x 30 = 390 days) and of T = 14 normalyears (of T = 12 months i.e. 12 x 30 = 360 days)39.

d.3.3) The average tropic year is kept at the value foreseen by Daicoviciu-Charriére scheme.

d.4) The urano-solar character of the Dacian religion 41 , was invoked as anargument for adopting a pure solar version of the presumed Getian-Daciancalendai42.

But starting from the axiom (basic thesis) that the (presumed) Getian-Dacian calendar was of a pure solar type, the logical thought reached anunsatisfactory conclusion: the numerology of the Great Circular Temple ofSannisegetusa may be organized in the framework of a scheme, but thisscheme presents incomplete connections with the appropriate observationaland mythological Getian-Dacian (presumed) astronomy.

d.4.1) The analysis between religion and main employment of thepopulation on a part, and the calendar officially in use on the other part,among some peoples in Antiquity, founders of relevant Mankind's culturesand civi1isations43 -namely the Egyptians, Chaldeans and Assyrians, Jews,Greeks and Romans- reveals real, but not obligatory, connections44.

d.4.1.1) The Egyptians had a polytheist urano-solar45 religion, they weretillers, and their calendar in use 46 was based on some astronomicalprinciples47.

d.4.1.2) The Chaldeans-Assyrians had an urano-solar religion 48 , they •were tillers, and their calendar in use 49 was based on some astronomicalprinciples50.

d.4.1.3) The Jews had51 a monotheist religion 52 , they were tillers,shepherds, fishers, and their calendar in use 53 was based on some astronomicalprinciples: they have used a luni-solar calendar54.

d.4.1.4) The Greeks had an urano-solar religion 55 , the_y were tillers,shepherds, hunters and navigators 56, and their calendar in use 57 was based onsome astronomical principles, they have used a luni-solar calendar.


d.4.1.5) The Romans had an urano-solar religion58 , they were tillers andshepherds 59 and their calendar in use was based on some astronomicalprinciples60, they have used61 a luni-solar calendar62.

d.4.2) The observation of the moon was, for all the considered cases 63 inhand", hence it was very convenient.

d.4.3) Thus the following question is to be accounted for why theDacians-Getians were so indifferent as concerns the moon's motion, the moreso as they had a goddess of Moon, of Forests and of Magic Practice65.

Our model of the (plausible) Dacian-Getian calendar from Sarmisegetusawas made respecting, strictly, the following methodological rules66.

a) It is recommended to take into account all the possible and plausiblecultural and economic influences underwent by Dacian area in the ancienttimes, and not to devise a calendar scheme that would conflict with theseinfluences.

b) It is recommended to favour the organizing of the Temple Numerologywhich may assign the best astronomical meaning to various pieces of thepresumed Calendar-Temple.

c) It is recommended to prefer, among several formal schemes ofreconstruction, that offering a maximal amount of astronomical information.

Using, in an appropriate manner, the afore mentioned archaeological,historical, numerological and astronomical data, and respecting the acceptedmethodological rules, we succeed:

a) to gather various kinds of arguments in view of malcing more likelythe luni-solar scheme of (supposed) Dacian-Getian calendar reconstruction;

b) to outline some methodological principles so that the adoption of aluni-solar scheme should not appear just as a free choice.

2. The (plausible) theoretical model of the (hypothetic) luni-solar Dacian-Getian calendar from Sarmisegetusa

Therefore, we are now in a position to proceed to our own schemeproposed as a (plausible) model of the (presumed) Dacian-Getian calendar fromSarmisegetusa. We begin our analysis by observing that a luni-solar calendarmust fulfil four basic functions, namely:

1) counting of days;


2) counting of months;3) correction to the month;4) correction to the year.

These basic functions are to be distributed among the N = 3 concentricfigures: the great circle, the intermediary circle, and the horseshoe. Thisdistribution must be made in an appropriate manner:

a) it is ascertained that:

a.1) the intermediary circle, and the horseshoe are closed curves almostentirely built-up of wooden 67 (oaken) thin pillars;

a.2) the great circle is built-up of a rigorous alternation of stone (large),and wooden (thin) pillars, amounting to 6 small wooden (thin) pillars for eachstone (large) pillar.

The special statute of the great circle seems to indicate that it is suitableto take over rather two than a single one of this four mentioned functions ofthe calendar, namely, that pair of functions able to account for the ratio N =

6/168 . We shall see later that these functions are the first two of the previouslisting.

b) The two curv.es having corrective role has different forms.•

b.1) The intermediary circle exhibits no visible derogation from a perfectgeometrical circle.This circumstance suggests 69 that the calendar function ofthis curve is related to the sun motion, i.e. this curve can be" the register ofthe tropic years.

b.2) The horseshoe enclosure71 is a heuristic materializing of the moonin one of its phases. The circumstance suggests72 that the (supposed) calendarfunction carried out by this curve is connected to the moon motion, i.e. thiscurve can be the register of lunations.

c) It is essential now to establish what is the luni-solar cycle, based onwhich an organizing of the Dacian numerology (in compliance with thefunctional correspondence between calendar and the elements of the Daciantemple -so as it was outlined above- should be possible. In this purpose weshall proceed to the analysis of the T = 8y, T = 1 ly and T = 19 years cycles73.


c.1) The Babylonian cycle of T = 8 years is the first remarkable scientificacquisition of the mankind in matters of calendar. It contains T = 99 lunarmonths and T = 2922 days, and is based on the algebraic equations:

12x + 13y = 99

29+3Oîi=2922

x + y = 8

+ ij = 99

whose solutions are the following ones:

x = 5 the number of short (normal) years, each containing T = 12 lunarmonths;

y = 3 the number of long (abnormal) years, each containing T = 13 lunarmonths;

1= 48 the number of short months, each containing T = 29 days;= 51 the number of long months, each containing T = 30 days;

By denoting the long and the normal years by A, respectively a, we cometo the following sequence for the repartition of the two kinds of years insidethe T = 8 years cycle:

aaAaaAaA

c.1.1) The two- characteristic data of luni-solar calendar, namely:

c.1.1.1) the average synodic period of the motion of the moon, Ti;

c.1.1.2) the average tropic year T2,

acquire the values: T1 = 29 + 51/99 days, T2= 365 + 1/4 days".

c.1.2) The succession of the months within the year is75:

c.1.2.1) All the years begin with a short month, T = 29 d76;

c.1.2.2) The short (1) and long (L) months are succeeded in an alternativeway until the correction month, i.e. the N = 33 - rd one is reached.

c.1.2.3) The correction month is a long month, L = TL = 30 days, insteadof a short month / = T1 = 29 days.

c.1.2.4) After the correction month, the normal alternating sequence ofmonths is taken over; beginning again with a short month, until thefollowing correction month is reached; and so on.


c.1.3) The years are:

c.1.3.1) The normal years made up of N = 6 short months, and N = 6long months, and, accordingly, containing T = 354 days;

c.1.3.2) The long years made up of N = 6 short months and N= 7 longmonths and accordingly, containing T = 384 days77.

c.1.4) The correction months are: (3, IX), (6, V), (8, XIII), where theArabic numeral indicates the year inside the T = 8 years cycle, while theRoman figure indicates the month in the respective year78.

c.1.5) The relevant conclusion to be drawn for our investigation from theexamining of the Babylonian cycle is:

c.1.5.1) The rendering evident of the magic number N = 33. As thisnumber, although close to the Dacian magic number N= 3479, is, however,different from this last number, we may conclude that the Babylonian cyclewas not used (as such) by the Dacians-Getians astronomers80.

c.1.5.2) The Babylonian cycle is not just the cycle we look for, but wemay still use it for finding the veryplausible cycle.

In this purpose we first observe that the duration of the calendar cycle,expressed in lunar months, is a small multiple of the magic number (in thecase of the Babylonian cycle: 99 = 3 x 33). Likewise, in the case of theDacian-Getian cycle, the duration of the cycle, expressed in lunar months,must be a small multiple of the number 34. Based on the Babylonian cyclewe may derive the approximative conversion relation T = 1 month = 8/99years and, accordingly T = 34 months = (8 x 34)199 = 272/99 years. Now, wereadily obtain: T = 4 x 34 months = 4 x 272/99 = 1088/99 = (11 - 1/99)years. Leaving aside the small fraction N = 1/99, which is surely due to someimperfections of the Babylonian cycle, with regard the astronomical real time,we infer for the duration of the Dacian-Getian cycle:

c.2) The (theoretically acceptable) Dacin Cycle is, TD = 11 years81 , formany reasons:

c.2.1) Because the next cycle (that of T = 19 years)82 seems toosophisticated, and, consequently, not suitable to be taken over by Dacians-Getians.

c.2.2) Because the N = 11 years cycle is standing 83 as a basis for theRoman calendar prior to the Julian reform 84. Thus we appreciate that there are


sufficient reasons to proceed to the examining of the cycle of T 11 years.This cycle contains T = 136 lunar months and T = 4016 days. It is based onthe algebraic equations:

12x + 13y = 136 29 + 3071 = 4016

x+y= 11 + = 136

whose solutions are: x =7, y = 4, = 64, ij = 72.

c.2.3) The average synodic period of the moon is T = (29 + 9/17) days29 53 days85.

c.2.4) The average tropical year is T = (365 + 1/11) days86.

c.2.5) Each cycle begins87 with a long month (T = L = 30 days), andends with a long month88.

c.2.6) It is divided into N = 4 identical subperiods, each having T = 34months89.

c.2.7) The correction month is a long month and it is placed at the end ofthe subperiod90.

c.2.8) Each subperiod begins with a long month and exhibits a regularalternance of long and short months, except for the last month (the correctionone); which is a long instead of a short one91.

c.2.9) After the spending of T = 68 subperiods (each having T = 34 lunarmonths), i.e. after the •spending of T = 17 Dacian cycles (each having T = 11years, and T = 136 lunar months)92 , it is necessary to add a long month (L =30 days) in view of correcting the tropic year.

c.2.10) The value of the tropic year, averaged over a period of T = 17 x11 = 187 years, amounts to: T = (4016 x 17 + 30)1 (I I x 17) = 365 + 1/11 +30 /187 = 365.251 days = the (theoretical) Dacian year.

This value has an astronomical accuracy similar to that of the Juliantropic year, established (in 46 B.C.) by the astronomer Sosigenes.

d) The test whether the explaining of the Dacian-Getian calendar in theframework of the T = 11 years cycle is possible will be given by thepossibility of accomplishing a global astronomical meaning of the Dacian-


Getian numerology together with a simple, and reliable, operation procedureof the presumed calendar.

We shall see not only that such a fitting is possible, but it is soimpressive that it seems quite improbable to be a simple occurrence.

The operation procedure of the (theoretical/pressumed) Dacian-Getiancalendar appears now simple, and natural, because the mnemotechnicalelements of the Great Circular Sanctuary of Sarmisegetusa are to be organizedin a luni-solar scheme in which the moon is directly pursued.

d.1) On the great circle, made up of 30 stone pillars, a certain marker ismoved, simulating the moon motion: it is running in the counter-clockwisesense.

d.2) We denote by 0 (zero) the starting (stone/large) pillar. If a lunationwould have just the duration of T = 30 days we will expect that, starting from0 at full moon we reach again the point 0 at the next full moon (running onetime through the circle). But actually a lunation is lasting about T = 29 1/2days, so that at the next full moon the marker will be placed not at the point0 (zero) but at the middle of the distance between the pillar 0 (zero) and thestone (large) pillar 29, the labelling being operated still in a counter-clockwisesense. More exactly: the marker will be located between the third and thefourth wooden (thin) pillars. In this way: while the marker ran in the counter-clockwise sense almost a complete rotation, counting the successive days of alunation (separated by stone/large pillars), the same marker ran in theclockwise sense only N = 1/2 of the separation distance between twoconsecutive stone pillars counting a lunation. At the following full moon,that is after N = 2 lunations, the marker will be placed at the stone pillarnumber N = 29; after N = 4 lunations it will be placed at the stone pillarnumber N = 28; and so on. Thus by this clever procedure: the same circle hasa double93 role, i.e. every running sense being endowed with a specificastronomical meaning. Correspondingly, the great circle of the Sanctuaryacquires a double labelling:

d.2.1) with Arabic numerals for days; associated to a trigonometric senseof running;

d.2.2) with Roman figures for lunar months; associated to a clockwiserunning.

d.3) A lunar month is divided (by wooden/thin pillars) in N = 3 decades,each decade having about T = 10 days94 . When the month had only T = 29days the third decade reduced correspondingly to a T = 9 days period.


d.4) The distance between two consecutive stone pillars represents 95 a T= 24 hours day, and such a day is divided, by the N = 6 wooden/thin pillarsplaced between the stone/large pillars, in N = 6 times96 . Assuming that theDacian-Getian day began at T = 6 o'clock p.m. time97 in order to performsatisfactorily the astronomical moon watching, we may establish thefollowing connection between the Dacian-Getian wooden/oaken/thin pillarsand the Sumerian parts of a day98:

l st pillar 18 h - 22 h Rising of Stars Bararitu2nd pillar 22 h - 2 h Zenith of Stars Qabditu3rd pillar 2 h - 6 h Twilight of Stars Sat urri4rh pillar 6 h - 10 h Sunrise Napakh Shamshi5rh pillar 10 h - 14 h Zenith Musla lu6rn pillar 14 h - 18 h Sunset Ereb Shamshi

e) The magic number N = 34 -incorporated in the structure of the GreatCircular Dacian Sanctuary and whose originality was appreciated asundeniable- it was known to many cultures and civilizations using luni-solarcalendars. But the meaning assigned to this number is not that of a correctionperiod of the synodic moon motion 99, but rather of a straightening out periodof a purely lunar calendar, still based on the T = 11 years luni-solar cycle.

e.1) To derive this m rneaning we proceed as follows:

e.1.1) We consider a purely lunar calendar whose year is made up of T =12 lunation.

e.1.2) Resorting to the T = II years cycle, we find:

e.1.2.1) the duration of the lunar year: T = 12 x 4016/136 = (354 + 6/17)days.

e.1.2.2) the duration of the tropic year: T = (365 + 1/11) days.

e.1.2.3) we reach the formula: T = one purely lunar year = (I - 1/34)tropic years, or T= one tropic year -one purely lunar year = 1/34 tropic year.

e.1.2.4) The obvious conclusion is that: the New Year of a purely lunarcalendar is sliding towards winter as compared to the New Year of a calendarbased on the tropic year, considering that we begin the counting of yearswhen the New Year of the two kinds of calendars are coincident. As thebackward sliding of the lunar calendar is T = (10 + 1/11 + 11/17)days for thespending of a single lunar year 101 , it follows that in 34 lunar years the New


Year of the lunar calendar is defiling through an entire tropic year (i.e. thesolar calendar), and, finally, is again coincident with a New Year, namely,with the New Year of the solar year N = 33.

e.2) The double role of the number N = 34 i.e. that of ensuring thecorrect value of the moon synodic period 102 and that of realizing a congruencebetween purely lunar and purely solar years may be an argument, at the levelof reasoning of the epoch for Dacians-Getians, and Celts, scientists &initiated priests to assign to this number a kind of magic value and, finally,to immortalize it by casting it in the structure of their temples.

f) After 34 lunations it is necessary (opportune) to add a day, in order toobtain a correct average synodic period of moon, because the very synodicperiod of moon is a little greater than 29 1/2 daysl°3.

For keeping in mind the instant of correction, every complete running ofthe marker on the great circle m (i.e. a lunation) is labelled on a pillar of thehorseshoe enclosure. As the horseshoe enclosure has just N = 34 wood(oaken) thin pillars it results that:

f.1) Moon period must be corrected every time when the horseshoe isfull.

f.2) Every filling up of the horseshoe is marked on a pillar of theintermediary circle.

f.3) Because the intermediary circle has just N = 68 wooden (oaken) thinpillars when the circle is full" a long period of T = 68 x 34 lunar months =17 luni-solar cycles = 187 = tropic years is elapsed, and the pontifices of theTemple became aware of necessity of correcting the tropic year (by adding alunation, as we already showed).

g) The astronomic meaning of the number N = 30 is (perhaps) to asmaller extent connected to the number of days in a month, but rather to thenumber of correction pillars on the great circle: this number is, indeed N =30, i.e. the number of all stone (large) pillars in the following order":

13, 26, 9, 22, 5, 18, 1, 14, 27, 10, 23, 6, 19, 2, 15,28, 11, 24, 7, 20, 3, 16, 29, 12, 25, 8, 21, 4, 17, 0.

h) The distribution of the long and normal years in a T = 11 years cyclecan be (plausibly) determined. This time we cannot detennine the distribution


of the different kind of years having in view (directly) the elements of theDacian-Getian round temple. But we can (plausibly) fill this lacuna by theappeal to the historical tradition in matters of calendar, and by taking forgranted that legends about the scientific knowledge of some Dacians-Getiansmen of culture 107 are not altogether inventions.

The existence of the (presumed) 108 Dacian-Getian calendar is a plausibleargument 1 °9 that, indeed, Dacians-Getians benefited of the astronomicalexperience of the Near East110.

h.1) We observe that the Jewish sequence l 1 1 giving the distribution oflong and nonnal years in a T = 19 years112 cycle, namely:

aaAaaAaAaaAaaAaaAaA

may be decomposed in two shorter sequences, namely:

aaAaaAaA+aaAaaAaaAaA

h.2) As the T = 19 years cycle 113 is based on a period containing T =235 lunations and T = 6939 days, the T = II years cycle, obtained bydecomposing the Jewish sequence, may be identified with the Dacian cycle.Indeed: 99 + 136 = 235; 2922 + 4016 = 6938. The missing day beingexplained by the fact that shorter cycles are more imperfect as compared tolonger ones.

h.3) We may, therefore, reasonably, assume that the long years (A), andnormal years (a) in the Dacian cycle of T = 11 years were distributed accordingto the sequence:

aaAaaAaaAaA

h.4) The Dacian sequence differs from the Babylonian one by an initialprimitive sequence (a a A), and satisfies, at the same time, the remarkableformula:

Babilonian sequence + Dacian sequence = Jewish sequence

i) A mnemotechnic procedure to mark the 11 years cycle can be found.As such, the spending of a cycle containing T = 11 years = 136 lunations, orT = 4 periods of 34 months, will be indicated by drawing on the great circleof a trapezium. The first such a geometrical figure inscribed on the great circle


has the corners at the points A (13, XXXIV), B (26, VIII), C (9, XLII), D(22, XVI). It is an isosceles trapezium whose symmetry axis may be taken tobe perpendicular on the line joining the centres of the two round sanctuaries:the great and the small one. When this circumstance is ensured then thestarting pillar used for reckoning days and months is placed in the Northerndirection, as reported to the centre of the Sanctuary114.

In this way a complete operational scheme of the (presumed) Daciancalendar, i.e. based on the Dacian-Getian numerology (6, 30, 34, 68) 115 , wasdevised, putting into evidence N = 3 registers of time reckoning, registerscorresponding to the N = 3 principal pieces of the (presumed) Dacian-Getiancalendar temple from Sarmisegetusa: i.e. 1) the great circle, 2) theintermediary circle, 3) the horseshoe.

This proposed theoretical model -i.e. archaeological-historical-astronomical model- can give, in our opinion, a satisfactory answer to almostall the calendar problems that may be raised in connection with the(presumed) Temple calendar of Sannisegetusa116.

Some constructive elements of the Temple 117 , are still outside thecalendar scheme put forward by us. In this situation are:

1. the exterior circle of the Great Round Temple118;2. the little round temple119;3. the Sun of andezitel".

The exterior circle made up of N = 104 andesite blocks, is pressed to theexterior side of the great circle made up of N = 30 stone pillars and theconstituent blocks are glued together resembling to the bricks of a wall. Theaspect and the position of the exterior stone circle, as well as the fact that N =

104 is a number without an astronomical meaning 121 , entail us to believethat the function of the respective circle is not astronomical, but rather aconstructive one: this circle being intented to be a simple protection wall.

The small circular sanctuary 122 equally has (probably) no calendarfunction, its role -similar to the role of the heel-stone from Stonehenge-being connected to the defining of the Northem direction.

We appreciate that our scheme of Dacian-Getian•calendar reconstructionhas many chances to be confirmed by further archaeological investigations,being, at the same time, a contribution to the knowledge of the ancientinhabitants on the Carpathian-Danubian-Pontic territory.


3. Some subsidiary comments

1. The first reference conceming a possible astronomical role of the GreatCircular sanctuary of Sarmisegetusa seems to come from D.M. Teodorescu,who made excavations during the year 1930. He assumed, in a time when notall the pieces of the Sanctuary were discovered, a relation between the 30-stone pillar circle and the moon motion.

2. Constantin Daicoviciu and his archaeological team, working duringthe years T = 1950-1958, succeeded to find out the pieces of the Great andSmall Circular Temples, and to give a complete and detailed description ofthese monuments123.

3. In T = 1960 Constantin Daicoviciu 124 put forward definitely thehypothesis •about the role of the Great Sanctuary as a system of time-reckoning, and introduced the denomination The Calendar-Temple of Dacians.At the same time he suggested a solar-type calendar of 360 days.

• 4. In T = 1963 G. Charriére introduced the corrective semester,T = 180days, at every period of • = 34 Dacian years (each year containning T = 360days, i.e. T = 12 months of 30 days).

5. In T = 1966 K&G Horedt put forward some strange hypotheses:

• 5.1. The calendar is based on T = 10 months, each of T = 36 days (thenumber of months being marked by the N = 10 circular sectors of the socalled Andesite Sun)125.

5.2. The division of the year was operated in two sessions:

5.2.1. A summer one, of T = 222 days, and

5.2.2. A winter one, of T = 138 days (motivated by the unequal sharingof the number of pillars of the horseshoe enclosure by the line joining thetwo sanctuaries).

6. In T = 1966, A. Popa made two interesting proposals:

6.1. The Dacian year began at the winter solstice126;

6.2. The 30-stone pillar circle of the Great Sanctuary represents a Dacianmonth, containing T = 30 days, while the N = 6 wooden/thin pillars betweentwo consecutive stone pillars, represent the divisions of a T = 24 hour day127.


7. In T = 1980 a research team of Brasov University composed by S.Bobancu, E. Poenaru and C. Samoila, devised a quite original and strangereconstruction of the (presumed) Dacian-Getian calendar, based on the idea thatboth Small and Great Circular Sanctuary from Sannisegetusa have a calendarfunction 128 . They conclude that:

7.1. Dacians-Getians had two calendars:

7.1.1. One of T = 365 days (based on the Small Sanctuary);

7.1.2. Another of T = 360 days (based on the Great Sanctuary).

7.2. The correction system of these connected calendars are also indicatedin this archaeological and numerological model.

7.3. The Rectangular Sanctuaries have also a calendar function.

The authors of this model of the hypothetical Dacian-Getian calendar usethe archaeological facts, but their model is purely numerological and not at allastronomical.

8. In T = 1983, on the occasion of the Scientific Symposium, devoted tothe 75th anniversary of the Astronomical Observatory from Bucharest, a firstversion of our scheme, concerning the supposed Dacian-Getian luni-solarcalendar was communicated129.

9. In T = 1984, Ioan Rodean published his book The enigmas of theSarmisegetusa stones in which some archaeological and cultural argumentsare gathered to support the idea that the Small Circular Sanctuary would be akind of: coded library of biorhythmology. At the same time, the authorinsists upon the constructive analogy between the Great Circular Sanctuary ofSarmisegetusa and the Stonehenge monument 130 , without inferring anastronomical conclusion. Other interesting idea, namely the correlationbetween the length of pillar shadows at noon and the solstice lines is,unfortunately, based on incorrect hypothesis that the equinoctium sunrise lineis rotated by the Precession of the equinoctia. In spite of many culturalacquisitions, mainly referring to geometrical symmetries, the reader comesacross many unreasonable assertions as we11131.

10. In the T = 1984, on the occasion of the Annual Meeting of theCentral Institute of Physics in Sibiu, the late prof. Victor Mercea from Cluj-Napoca 132 related the success of a magnetornetery team managed by himself


who put in evidence the existence of a new circle (made up of holes) exteriorto the Great Circular Sanctuary133.

11. The astronomical directions of the place were studied by prof. Gh.Chis from University Babes-Bólyai of Cluj-Napoca.

12. At the end of T = October 1984 an interdisciplinary team (made up ofarchaeolbgists, topometers, architects, engineers, a.s.o) pertaining to theAssociafion of Scientists executed measurements at Sannisegetusa in view ofconfirming what they called The numerical system of Geto-Dacians devisedby Timotei Ursu and Florin Stanescu134.

13. The calculation of the charasteristics of the astronomicalobservations at Sarmisegetusa Regia has been made by using the followingangles, relations and data:

13.1. The angle of maximal ascension of the sun at the equinox: tPe.n.

13.2. Idem at the summer solstice, respectively at the winter one:

Tw•s.

13.3. The geographic latitude: oc.

13.4. The angle of the inclination of the axis of the geographic poles onthe ecliptic: 8.

13.5. For Sarmisegetusa we have: N = oc 45 037, N = 8 23°0, withthe correction of the oblicity:

N = e.n a44°23'

N = 111 = —2

- a+ = 67°23'

N= = - a- 21°23'2

13.6. Because Sarmisegetusa is located in an area with mountains withan important horizon height, the directions of the sunrise in different days ofthe year are sensibly modified with regard to the homologous directionscalculated at the sea level. Let be: x the angular height of the horizon, and,


accordingly: x i the angular height of the horizon in the point where the sunrises at the summer solstice, x 2 the angular height of the horizon in the pointwhere the sun rises at winter solstice.

13.7. The angles between the direction East at the equinox (at sea level)and the directions of the sunrise at the equinox (at sea level) at the summerand winter solstices are:

Cle.n =

65s.s = (Zw.s =

Due to the height of the horizon (determined by the relief) atSarmisegetusa the homologous angles are:

S XO (0 e.n — ) — - Xo tg

tgk-2 - a

S X1 W s.s —

8 - xi tg(a - 8)tg(y - a + 8)

toSw.s = 8 0 X2 — - X2 tg(a

tg(I - - 8)

In acordance with the topometrical measures we have:

N = x i 7°12, N = X2 6°7 , N = Xo 7°44,

ASN = coe, 7°44 • tg(45°37') = - 7°54'

SN = oks 23°0' - 7°12' • tg(22°37') = 23°0' - 3°0' = 20°0'

N = cow . s - 23°0' - 6°7' • tg(68°37') = - 23°0' - 15°37' - 38°37'

13.8 The angle between the north direction and the direction of thesunrise at the winter solstice is:

N = = 900 + 38°37' = 128°37' 129°


The exactitude of this value is acceptable:

a) In [GLODARIU, IAROSLAVSKI, RUSU, 1989 p. 115, fig. 16] onecan found the plan of the great round sanctuary of Sarmisegetusa. Measuringthe angle between the north direction and the axis of the stone slabs in therespective figure is obtained 129°.

b) In the same book it is given a very plausible argument to support theidea that at Sannisegetusa there was a centre of astronomical studies: namelyit is advanced the idea that the Sun of andesite could have functioned as agnomon, in the sense described in the IXth book On time measuring byarchitect Vitnivius.

c) The determination of the angle between the north direction and the axisof symmetry of the Sanctuary is in qualitative accordance with the measuringmade by I. Carnaru and I. Ghica (1986): they obtained 123°.

d) It is also to be mentioned that we have made corrections taking intoaccount the fact that the inclination of the geographical poles axis in theantiquity was (presumably) a little different in comparison with that of today(due to the variation of the ecliptic obliqueness).

e) It is to be mentioned the fact that in winter, when the woodssurrounding the sanctuary became transparent, the height of the horizonproduce a little decreasing of the value of the angle N = 129°.

f) The coincidence between our calculations and measurements can bemade with a more satisfactory precision having in view, in connection to theseason variation xi of the height of horizon (i.e. ôx i ; i = s, w), also:

f.1) The secular variation of the inclination of the polar axis (5 P a) due tothe oscillations of the ecliptic plane with a period of T 4 x 104 years;

f.2) Some possible shifts of the Earth;

f.3) Some imprecisions in the determination of the centre of thesanctuary and that of the geographic direction of the North.

f.4) The corrections due to the obliqueness of the ecliptic produce thedecrease with N = 1 0 in T = 4000 years of the angle N = 23 027 135 . For aperiod of T = 2000 years we have to consider a correction of = 27.

f.5) Due to the precession of the axis regarding the normal against theecliptic plane with a period of T 26000 years, it is not necessary to do any


correction because the combined effect of this precess and that of the motionof the Earth on the ecliptic reduces only to a millennial shifting of the vernalequinox from a constellation to another.

f.6) It is true that the North celestial pole, which at present is in Polaris(i.e. ot Ursa Minor) was T = 2000 years ago in Dragon, but once the directionof the North is well established at a given epoch on the basis of the respectiveposition of the celestial North pole (i.e. the star, whose circle of declinationhas a null radius) then this North direction remains unchanged for any comingepoch, and -together with that- the sunset directions of the sun at thesolstices.

f.7) Unfortunately, the line on the ground which really must be identifiedwith the Dacian-Getian Northern direction is unknown. Nevertheless, with acertain plausibility, this line seems to be the line starting from the centre ofthe Andezite Sun and passing through the axis of one of the little rectangulartemples 136 . We can give an error of E 2° in the determination of thedirection of the North by the Dacians.

f.8) The shifting of the geological deposited layers must be determined onthe basis of special geographical studies to establish if they really occur.

f.9) It cannot be excluded also an increase in T = 2000 years of theheights of the horizon (in the direction of the astronomical interest) due to thedust deposits produced by the strong winds.

14. The attempt to find parallel cultural lines to Dacian-Getian and Mayacivilisations seems unlikely, for many reasons:

14.1. Because the Sarmisegetusa monument is much older than theCopan Observatory in Honduras;

14.2. Because no possibility existed for a cultural intercourse between thetwo cultures and civilisations:

14.3. Because the two cultures and civilisations developed on quitedifferent lines, determined by quite different historical circumstances. Someeventually numerological astronomical coincidences must be judged as such,as pure coincidences.

15. In spite of this clear situation, we may identify easily the tendency ofa certain Maya influence.

15.1. The S. Bobancu, E. Poenaru, C. Samoilá team speacks about twoDacian calendars: the religious and the civil one.


15.2. Allusive references to Maya culture are still to be found to IoanRodean.

However we have not to overlook the presumptive character of the Mayacalendars actually they being nothing but a reconstruction due to thearchaeologist Eric Thomson 137 . The Maya calendar (based on a T = 260 daysyear) is specific for the observatories placed in the proximity of the tropic.The correspondence between the two Maya calendars is : T = 52 years of T =365 days = 73 years of 260 days; i.e. the so called Maya period.

We find no reason to identify a Maya period T = 52 = 104/2, N = 104being the number of stones in the exterior wall of the great circular sanctuary-to Dacians-Getians who were living far from the íropic.

16. Another idea (also put in circulation by Ioan Rodean) used for acorresponding reconstruction of the Sarmisegetusa sanctuaries, is that themiddle circle of the great round sanctuary has not 68 wooden/thin pillars but84!

Although this assumption is not yet a certitude, we must examine alsothe consequences following from it: if we assume a certain, i.e. not exactlyknown, number of pillars in the respective circle we obtain the followingtable for the values of the correction period and the average tropic year:

No. of pillars 64 68 72 76 80 84

No. of years in a period 176 187 198 209 220 231

Average tropic year (days) 365+0.261

365+0.251

365+0.242

365+0.234

365+0.227

365+0.221

16.1. We ascertain that, unlike other schemes, our reconstruction of theDacian-Getian calendar does not contain the number N = 68 as a critical one.

16.2. The precision of the average tropic year is good enough for anyvalue of the number of wooden pillars lying in the range 64 N 84.

16.3. To notice however that an exceptional accuracy is obtained for N =72. In this case the Dacian average troptc year would differ from the


astronomical value only by T = 2 x 104 days over a period of T = 2 x 102years, i.e. an error of T = 1.0 x 10 6 daysiyear.

17. An open question is the New Year of the hypothetical Dacian-Getiancalendar. The remark made by A. Popa that Dacian Year began at the wintersolstice is based on the ascertainment that the axis of the Dacian-Getianhorseshoe enclosure makes an angle of about N 25 6 with the West-Eastline. However the orientation of the horseshoe does not necessarily imply thementioned conclusion about the New Year, for the very reason that therespective angle of N 25° not only reveals the sunrise direction at thewinter solstice, but, equally, the sunset direction at the summer solstice.

As far as a luni-solar scheme of the calendar is accepted it is quiteplausible to assume that the Dacian New Year was celebrated in the eveningbefore the surnmer solstice at T = 18h (1.m.t). But this was possible a singletime in an T = 11 year-cycle, namely at the beginning of the cycle. For otheryears of the cycle the New Year had an oscillation in the proximity of thesummer solstice (not exceeding about T = 14 days).

18. Perhaps the most serious objection against the interpretation of theGreat Circular Sanctuary as a calendar is the fact that the Sannisegetusasanctuary, unlike Stonehenge Sanctuary, does not benefit of a free horizonnecessary for observing the sunrise at different seasons of the year.

• But if Dacians-Getians were able to observe the sunrise instant at sealevel they were able to determine the Northern direction and the equinoctialday tiy pursuing the length and the direction of the shadow of a certainreference pillar.

The steps of this procedure are the following:

18.1. They would observe that from the sunrise till to sunset thedirection and length of the shadow is continuously changing;

18.2. The shortest shadow of the pillar is recorded at the noon (when theascension of the sun on the sky is maximal);

18.3. The direction of the shortest shadow does not change when isgoing from winter to summer (the Northern direction);

18.4. At a certain day of the year the shortest length of the shadow isjust equal to the length of the piltar: this happens two times in a year, and


every time the sunrise direction is perpendicular on the Northem direction. Asthe Sarnaisegetusa Sanctuary is at latitude of about N = cs = 45 0 N, the twodays correspond to the two equinoxes;

18.5. The Dacians-Getians astronomers could observe the quality of thelight-time and the dark-time at an equinoctial day.

19. It is possible that also the Small Circular Sanctuary should be,somewhat, connected to the four seasons of a year. If we start from theNorthern direction of the sanctuary and nin in a trigonometric sense on thecircle, we come across the following groups of pillars (separated by a pillar ofdifferent type): 7 groupings of 8 pillars each, 1 grouping of 7 pillars, 3groupings of 8 pillars each, 1 grouping of 6 pillars, 1 grouping of 8 pillars.Now, if we count in the trigonometric direction the first N = 12 groupings weobtain 93 wooden (thin) pillars. The following N = 11 groupings give then N= 87 wooden (thin) pillars. In the clockwise direction the counting gives N =93 pillars and still N = 93 pillars (for two times 12 groupings). Finally, weobtain the following comparative table138:

A. TRIGONOMETRIC SENSE

1) first 12 groupings 93 pillars23 Sept. - 22 Dec. (91 d)

2) following 12 groupings 87 pillars23 Dec. - 22 March (89 d)

B. CLOCKWISE SENSE

1) first 12 groupings 93 pillars21 March - 21 June (93 d)

2) following 12 groupings 93 pillars22 June - 22 Sept. (93 d)

TOTAL 366 pillars, 366 d

The beginning of the counting with the Northern stone of the Sanctuaryat 23 September (i.e. an equinoctial day), may be correlated to the Northerndirection of the shadow at the noon (when the shadow length and the pillarlength are equal).

20. The horizon height at Sarmisegetusa is a difficult question whichmay be invoked as an argument against the astronomical destination of theround temples.


20.1. According to the topometric measurements, the angular heightversus • the angle between a line joining a reference point to the observer andthe West-East line is given by the table:

•T x T x T x T x

EO° 7°44 N90° 14°25' W180° 11°42' S270° 6°55'

10 0 7044' 100° 17°27' 190° 10°31' 280° 5°18'

20° 7°19' 110° 15°34' 200° 11°18' 290° 4°54'

300 6°55' 120° 15°57' 210° 10°31' 300° 3°15'

40° 10°07' 130° 17°27' 220° 8°56' 310° 3°16'

50° 10°55' 140° 15°34' 230° 8°56' 320° 4°30'

60° 11°42' 150° 15°57' 240° 5°18' 330° 6°07'

70° 12°53' 160° 15°57' 250° 4°54' 340° 6°07'

80° 14°02' 170° 14°02' 260° 4°54' 350° 6°55'

E360° 7°14'

20.2. As the angle between the equator and the ecliptic is N = 8 =23°2654.2, while the latitude of Sarmisegetusa is N = oc = 45°4516, weobtain the following situation of the declination, angles, referring to thesunrise line at solstices and equinoxes:

Satx=0 8atx � 0

summer solstice N = 8 = 20°2054.2" N = 8 = 20°2648.2"

equinox N=8=0° N = 8 ,-7°5323.0"

winter solstice N = 8 = -23°26'54.2" N = 8 = -38°25'59.2"

20.3. These dates are still to be corrected because the Northern directionused in the topometric works was determined by the magnetic needles. Themagnetic declination, is about N = 1°E, with a tendency of increasing theeastern displacement. At the data of topometric measurements (17 Apj-il 1982)it is likely to assume a magnetic declination of about N = 1°30El39.

496 LIVIU SOFONEA Y NICHOLAS IONESCU- pALLAS LLULL 17

21. Concerning the origins and the possible masters in astronomy of theold Dacians we will note here two mentions dating from the end of the 19thcentury:

21.1. Zamolxis avait beaucoup voyagé et de trés bonne heure. 11 avaitvisité tour á tour les terres classiques de l'Orient, avait séjoumé en Egypte,chez les Juifs, en Chaldée, s'instruisant aprés • des sages de ces contrées,interrogeant leurs devins et leurs prétres, se faisant initier aux mystéres qu'ildevait introduire plus tard ches les Gétes [H. Ubicini]14°.

21.2. L'origine des Daco-Gétes a été controversée. On s'est efforcé de faired'eux, tour á tour, des Germains de souche gothique (Jordanes, Jacob Grimm,Carlo Troja, Ozanem, etc.), des Celtes (Pezron, Wachter, Pelloutier, Fr.Miiller, Maiorescu, etc.), des Slaves (Bielowski, Zachariev, Vercovitch et laplupart des écrivans russes et polonais). Aucun de ces systémes ne résiste á unexamen sérieux. L'opinion intermédiare de M.M. Henri Martin et JeanBratiano, B.P. Hasdeu, qui voient dans les Daces de demi-Celtes (Gallo-Gétes)sortis du mélange des indigénes avec les peuplades gauloises environnantes,pardit plus vraisemblable [J.H.A. Ubicini] 141 . To notice that the strikingsimilarities of the symmetry elements of astronomical meaning at Stonehengeand Sarmisegetusa sanctuaries do agree with the Gallo-Getic hypothesis aboutthe origin of Dacians142.

22. For the shadow diagram, we have used the formula:

x _ 1 -vi (cosy)2 + (tg9)-21 siny

where: cp -the angle of the hour (in the apparent plane of the trajectory ofthe Sun); y -the angle of the season (the inclination of the apparent plane ofthe solar trajectory).

22.1. For the relevant data we have:

21 June; lat = 45 0 N 22 December; lat = 45°N

mr = 45° + 23° = 68° xti = 45° - 23° = 22°

1 = 1 =1.0785347 <0.1403301 + (tgq)) 2 2.6694671 <0.8596699 + (tg9)-2

LLULL 17 ASTRONOMICAL MODELLING OF THE LIFE OF DACIANS-GET1ANS 497

22.2. For different angles:

cp = 15 x/1 = 4.04537 cp = 15 x/1 = 10.26544

q) = 20 x/1 = 2.99067 (p= 20 x/1 = 7.74067

(1)=30 x/1= 1.91127 (p= 30 x/1 = 5.24447

cp = 45 x/1 = 1.15173 cp = 45 x/1 = 3.64034

cp= 60 x/1 = 0.74228 (p= 60 x/1 = 2.91572

q) = 80 x/1 = 0.44655 (p= 80 x/1= 2.51945

cp = 90 x/1 = 0.40403 cp = 90 x/1 = 2.47509

cp = 100 x/1 = 0.44655 (I) = 100 x/1 = 2.51945

(p =120 x/1 = 0.74228 (p=120 x/1 = 2.91572

cp =135 x/1 = 1.15173 (p=135 x/1= 3.64034

(p = 150 x/1= 1.91127 cp = 150 x/1 = 5.24447

cp = 160 x/1 = 2.99067 cp = 160 x/1 = 7.74067

q) = 165 _ x/1 = 4.04537 cp = 165 x/1 = 10.26544

23. The topic the old Dacian-Getian monuments of Sarmisegetusa Regiahas generated many controversial answers and interpretations. Of relevantinterest are those referring to the aspects less known, or even enigmatical and,a fortiori, those referring to the cases of open problems: mainly thediscussions with regard the covered with roofs/uncovered form of thetemples143.

Some authors put forward the following versions 144 : of thearchaeological initial form of the round and rectangles sanctuaries fromSarmisegetusa all the temples were completely (sic!) covered, in such amanner that no one element (i.e. neither the wooden/thin pillars nor thestone/wide and flat ones) were visible. • On the contrary, they all wereengraved: because it is assumed that they have been used exclusively formaintaining the stability of the buildings.

But even in this case some relevant astronomical-geographical directionscould be, appropriately marked 145 if the practical, or the conceptual necessityshould impose this request.

498 • LIVIU SOFONEA Y NICHOLAS IONESCU-PALLAS LLULL 17

24. In the frame of the problem of the connection between thearchaeological Dacian monuments and the astronomical knowledge attributedto some clever Dacian-Getian priests, some authors make mention of apossible, even plausible, use of the gnomon in that cultural area.

But they do not mention, as direct or indirect proof:

a) any effective astronomic result;b) the existence, or the non-existence of a Dacian-Getian calendar;c) the original -or the imitation- type of this very necessary social,

economical, religious, scientific tool.

We are deeply indebted to anyone which can give their constructivecritical observations or suggestions, so that to improve these plausibleastronomical considerations.

Figure 1. Plan of the archaeological situs at Stonehenge.


•

Figure 2. Diagram for visualizing the hypotethical Dacian-GetianCalendar of Sarmisegetusa Regia functioning according to our reconstructionscheme.

M: An appropriate marker moved by men.

The marker M moved by men in orthograde sense ensures themeasurement of days; each day is divided in N = 6 time fractions.

The marker M moved by men in anti-orthograde sense (watch sense)ensures the measurement of months; each month is divided in three decades(fractions).

The lunation is: T = 29 1/2 d; with a correction at the T = 34 lunatios.The positions A, B, C, D indicate the months when is necessary to make thecorrection. The first month has T = 29 d.

Line ofe2uinocha


Figure 3. Horseshoe orientation and sunrise lines at different seasons inboth Sarmisegetusa and Stonehenge Temples (all the topographic detailsconcerning Sarmisegetusa were obtained by the courtesy of dr. ing. KissArpad, from the Topography Department of the University Transylvania fromBrasov.

111I1 i I120° 140°

1 • 1

o° 20° 40° 60° 80° 100°

I I

160° 180°

LL1ULL 17 ASTRONOMICAL MODELLING OF THE LIFE OF DACIANS-GETIANS 501

Figure 4. Shadow diagram at Sarmisegetusa.

The longer lines represent the dimensions of the shadows at the wintersolstice, the stiorter ones are at the summer solstice; at the noon, the shadowsare N = 0.404 times the pillar lenght. To notice the resemblance between theshadow diagram and the mysterious horseshoe enclosure.


Figure 5. The apparent motion of the Sun at 4.5° northern latitude.

(Zi, Z2, Z3) stand for the zenith position of the Sun at winter solstice,vernal equinox and summer solstice. (Ri, R2, R3) stand for the sunrise at thesame astronomical days, for a zero height of the horizon. (S S2, $3) are thesunset positions for the three dates of the year. (R 1 , R'3 ) are the sunrisemodified positios due to the horizon height at Sarmisegetusa. S 1 R 1 linecoincides with the Round Temple axis going through the horseshoe enclosure.0 is the observer placed at the centre of the Temple.


line of apparent motion ofthe Sun (hiden in the regionAC by the horizon heigth)

Figure 6

The horizon correction:

cTA •TB "c7c R

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BC K2 , le2 tg 114.1 = A=73 = tg visd

j3 is the exceeding angle to be added to 5 in view of accounting for thehorizon height.

504 LIVIU SOFONEA Y NICHOLAS IONESCU-PALLAS

LLULL 17

01 234 5 6 ? 8 mti•It

Figure 7. The Calendar sanctuary of Sarmisegetusa. Plan and essay ofreconstruction. /without the respect of numerical data/Apud H. Daicoviciu/op.cit.

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NOTES

1 In our vision, which is an axiological one -i.e. the Imago Mundi ofHomo Humanus.

a) The culture is the dynamic set of autotelic values: Truth, Good, Beauty(i.e. the essays and the achievements of Homo Sapiens Scientiae, Homo Cogitans,Homo Aestheticus, Homo Religiosus, Homo Philosophans).

b) The civilization is the dynamic set of mean values: Political,Economical, Technical-Technological, Ergonomical et al., i.e. the eSsays.

2 See reference 1, especially the part a).Peoples which had in Antiquity some contacts; some of them are

attested; others are only conjectured.Others civilizations and cultures like those developed during the

Antiquity in the Far East Asia, in the pre-Columbian America et al. had their owndevelopment.

3 In many cases, greatly exceeding a life expectation of 50 years (Platon,Charmides).

4 As we shall argue in this historical-epistemological work.5 We note different astronomical periods with T, but without other

indices. In some special cases the specific indices will be used.We note different astronomical numbers with N. In general without

others indices; in some special cases the specific indices will be used.6 _ lst century B.C. -/1 st century A.D.7 I.e. of Babylonian type.8 Year of the Julian reform.9 Namely of T = 355, T = 377, T = 378 days.10 This is the most plausible reconstruction; the integers x, y, z are

uniquely determined.11 At least in this model based on the archaeological details of this central

monument only. See [DAICOVICIU, 1972, pp. 232-266].1 2 According to some serious historical sources, Herodot, et al. See

[SOFONEA-IONESCU, 1993, p. 38].13 Or (presumably) was in contacts with.the sources of ancient astronomy

Strabon.As is mentioned by Jordanes and Hellanicus. See [SOFONEA-IONESCU,

1993, p. 38].14 According to some serious historical sources, Herodot, et al. See

[SOFONEA-IONESCU, 1993, p. 38].15 Or (presumably) was in contacts with the sources of ancient astronomy

Strabon.As is mentioned by Jordanes and Hellanicus. See [SOFONEA-IONESCU,

1993, p. 38].16 As was related in 1968 by MSF Hood. See [SOFONEA-IONESCU, 1993,

p. 38].17 Discovered in the Jemdet Nasr excavation site.18 Coming from Knossos.


Quite recently (about T = 1984), such tablets with cuneiform writingwere discovered in an excavation site near Bucharest, strengthening the opinionthat their presence on the Carphatian-Danubian-Pontic territory is not a randomevent.

19 By MSF Hood. See [SOFONEA-IONESCU, 1993, p. 38].20 By V. Gordon Childe et al. See [SOFONEA-IONESCU, 1993, p. 38].21 To notice that the Tartaria village, where the aforementioned cuneiform

tablets were found, is placed in the region of this culture.22 Undertaken by us et al.23 A detailed presentation of this study will be in this work.24 Scientific activites were intimately connected-influenced by religion in

pre-Antiquity and long time later.25 About astronomy.26 The neighbours of Dacians-Getians in the Buerebista Epoch.27 Undertaken by G.S. Hawkins in 1963-64, and by Fred Hoyle in 1972, et

al. See [SOFONEA-IONESCU, 1993, p. 38].28 Which have the same number (and, presumably, the same function, too)

in Stonehenge and Sarrnisegetusa.29 Unlike some of the previous enterings upon which disregarded the large

stone pillars assigning an astronomical meaning only to the small woodenpillars.

I.e. those made by C. Daicoviciu, G. Charriére, D. Antonescu. See[SOFONEA-IONESCU, 199, p. 38].

30 It is compulsory to notice here that the hypothesis concerning themoon's motion as basic element for deciphering the calendar of the great sanctuaryof Sarmisegetusa is not quite new: it was put forward by M.D. Teodorescu (1930-31). See [SOFONEA-IONESCU, 1993, p. 38].

Nevertheless the lack of direct, i.e. reliable arguments, as well as thelack of a genuine correlation of date pertaining to different appropriate fields ofscientific activity able to obtain the necessary proofs, entitled, in 1972, H.Daicoviciu to reject the respective hypothesis as a groundles one. See[DAICOVICIU, 1972, pp. 232-266].

31 A special role in the history of the subject we come to enter upon is amodel of a calendar devised by a research team from Brasov University: S.Bocancu, C. Samoila, E. Poenaru). This construction is, doubtless, an enticingone, by both the reached accuracy and the boldness of including in the projectelements of economic and social life of Dacians. However, the construction is, onthe whole, strange enough, just due to its small connection with the astronomicalelements which, as was ascertained, constituted a general trend of the ancientcalendars. See [BOBANCU, SAMOILA, POENARU, 1978, pp. 1-150].

32 Some epistemological, as well as some cultural comments were made byL. Sofonea. •

33 It is only an analogy. Bui the role of the analogies in the adventure ofthe science is impressive.

34 Relying on archaeological facts, astronomical data and historical events(i.e. archaeology: as scientific research of the characteristics of the old


civilizations and cultures, of their features, historical dimensions and reciprocalinfluences).

3 5 The presumed connection between the big round sanctuary and the smallone consists in the fact than in the big monument it is a way marked by stoneslabs having a parallel direction with the basis of the horseshoe, and theextension of this very passage roughly reaches the little sanctuary.

We observe that to Stonehenge the connection line is not parallel withthe basis of the horseshoe but perpendicular. This situation can, eventually,suggest that the beginnings of the years at Stonehenge and Sarmisegetusa wereshifted with a half of year. It is assumed that the midsummer sunset line is stronglyassociated with the symmetries of the archaeological monument (see fig. 1).

3 6 It may be conjectured that in the past the coincidence was still morestriking, but during the time some uncontrolled ground slidings presumablyhappened at Sarmisegetusa.

37 34 x 360 + 180 = 34 tr y1 tr. . y = 360 + 180/34 = (365 + 5/17) days

3 8 A kind of subsidiary time division, necessary for the self-consistency ofthis project.

39 t = 3 + 14 = 17 years; T = (3 x 13 + 14 x 12) = 207 months.40 t = 3 + 14 = 17 years; T = (3 x 13 + 14 x 12) = 207 months.

T = 207 x 30 = 6.210 days; T = 6210/17 = (365 + 5/17) days = I tropicyear.

We cannot deny a certain attracting feature of this version of the Dacian-Getian calendar: altogether original by its non resemblance with known (attested)schemes of time-reckoning. But, presumably, it is just this originality (at anyprice) which may put under a mark of doubt the reality of this clever scheme.

4 1 I.e. the adoration of sun, moon, and of certain brilliant stars.Perhaps a proof of a certain syncretism, despite of their (presumed)

monotheism, enthusiastically backed up by the archaeologist Vasile Párvan.42 Feature supported by archaeological, historical and logical arguments.

This kind of arguments is clearly exposed by Hadrian Daicoviciu in his monographissued in 1972.

43 And surely having intercourse with Dacian-Getian culture andcivilisation.

44 No such rule can be formulated.45 Mainly.46 I.e. the official one.47 The rise of the star Sirius (named Sephedet) and the flux and reflux of the

level of water on Nylus, determined by the climatic seasons.This topic is treated in all General Histories of Science, see, for•

instance: General History of Sciences, under the redaction of R. Taton, vol. I, Ed.Enciclopedia, Bucurepti, 1980.

48 Mainly.49 I.e. the official one.50 Observations of the rises, and of the sets of sun, moon, and also some

stars.5 1 From very early times.

LLULL 17 ASTRONOMICAL MODELLING OF THE 1JFE OF DACIANS-GETIANS 509

52 Mainly.5 3 I.e. the official one.54 This topic is treated in all General Histories of Science, see, for

instance: General Histoly of Sciences, under the redaction of R. Taton, vol. I, Ed.Enciclopedica, Bucuresti, 1980.

Preserved and improved during the centuries, up to the present times.55 Mainly.56 Mainly.57 I.e. the Official one.58 Mainly.59 Mainly.60 Preserved and improved during the centuries, up to the present times.61 Mainly.62 The suppressing of the Roman luni-solar calendar under the rule of Julius

Caesar (T = 46 BC) was determined rather by political reasons, in view ofdecreasing the influence in Senate of the pontifices from the Calendarcommission. •

See for instance Encyclopaedia Britannica (the word calendar).63 We find that there are reliable rules: from general logical and

methodological point of view, from the (plausible) archaeological, historical,numerological and astronomical point of view.

64 I.e. the compatibility, which is a sine qua non condition of this kind ofmodels.

65 Diana-Bendis.66 We find that there are reliable rules: from general logical &

methodological point of view, from the (plausible) archaeological, historical,numerological and astronomical point of view.

67 Excepting some stone thresholds, whose function does not appear asdirectly connected to the calendar operation.

68 Which is an archaeological fact.69 I.e. advocates the adopted hypothesis.70 I.e. advocates the adopted hypothesis.7 1 As a figure.72 I.e. advocates the adopted hypothesis.73 These cycles Ti , i = 1, 2, 3, are obtained as three successive

approximants -Ni = (99/8, 136/11, 235/19}- of the continued fraction of the ratiobetween the tropic year and the synodic month: N = 365.2422129.5306.

To notice the missing of the T = 13 years, and of the T = 17 yearsperiods, used by E. Poenaru et al., and by D. Antonescu. See [SOFONEA-IONESCU,1993, p. 38].

74 2922/99 = (29 + 51/99) synodic lunar period, 2922/8 = (365 + 1/4)average tropic year.

7 5 This succession is proposed for a best pursuing of the astronomicaltime.

76 This succession is proposed for a best pursuing of the astronomicaltime.

77 6 x 30 + 6 x 29 = 354


6 x 29 + 7 x 30 = 38478 As it follows from the step by step reconstruction of the cycle.79 34: the horseshoe number.80 This does not preclude, however, the taking over, by Dacians-Getians,

of many elements of the Babylonian calendar, as we shall later on relate.81 Which is the main idea of this theoretical model.

The number N = 11, as it was shown, is an astronomical number.82 The number = 19 has also an astronomical meaning: it is the next

approximation in the calendar calculation.83 In full probability.84 And the cultural dialogue between Dacians-Getians and Romans was

intense enough.Properly speaking, the Roman Calendar of the Republican era was not a

luni-solar calendar, but reminiscences of an early such calendar were preserved.85 401.6 : 136 = 29 + 9/1786 4016 : 11 = 365 + 1/1187 As suggests the step by step reconstruction.88 Again for a best pursuing of the flowing of time.8 9 Again for a best pursuing of the flowing of time.90 Again for a best pursuing of the flowing of time.91 Again for a best pursuing of the flowing of time.92 68 x 34 = 2312 months; 2312/136 = 17 cycles.93 Practically, as well as philosophically, the left and the right are not the

same, but despite any difference, they are intimately connected.94 As it necessarily follows from this interpretation of the operation

mechanism of the (presumed) Dacian-Getian calendar. Such a situation may befound, for instance, in the ancient Greek calendar, where the Hebrew 7 days weekwas not known and the month was divided in N = 3 decades:

- the first decade urlv icrrauevos- the second decade (not especially denominated)- the third decade Kriv (peivow.

95 Marked by the position of the same marker -but with the sense ofmotion considered in the counter clockwise running sense (i.e. in thetrigonometric sense).

96 Just as in the Sumerian calendar. Just as to some Jewish communitieswhich use the old calendar.

97 To notice that these divisions of a 24 hours day are, to day still, to befound in the folklore tradition of the Romanian people; namely: 1) Seara(Evening), 2) Miezul Noptii (Midgnight), 3) Revarsatul Zorilor (Daybreak), 4)Dimineata (Morning), 5) Prinzul (Noon), '6) Chindia (Aftemoon).

98 To notice that these divisions of a 24 hours day are, to day still, to befound in the folklore tradition of the Romanian people; namely: 1) Seara(Evening), 2) Miezul Noptii (Midgnight), 3) Revarsatul Zorilor (Daybreak), 4)Dimineata (Moming), 5) Prinzul (Noon), 6) Chindia (Aftemoon).

At the same time we have to remember that not only in AncientMesopotamia, but equally in Ancient Greece and Ancient Israel, the beginning ofday was in the evening.

LL1JLL 17 ASTRONOMICAL MODELLING OF THE LJFE OF DACIANS-GETIANS 511

99 As in the theoretical model of (plausible) Dacian-Getian calendar.100 Second.101 (365 + 1/11) - (354 + 6/17) = (365 + 1/11) - (355 - 11/17) = 10 + 1/11 +

11/17102 Namely T = 29.5306 days.103 Namely T = 29.5306 days.104 I.c. a lunation: TL.105 I.e. the marker has made a complete tour.106 The step being 13.107 Zamolxes, Deceneu, and also (presumably) other ones.108 At present almost a certitude.109 Even a peremptory one.110 Either directly or through the agency of Celts.111 Discovered by the astronomer rabbi Hillel.112 I.e. Meton cycle.113 I.e. Meton cycle.114 This peculiarity of the Temple construction does not seem to be a simple

hazard!.115 See [DAICOVICIU, 1972, pp. 232-2661.116 And a fortiori of sacred Area of Sarmisegetusa Regia.117 And a fortiori of sacred Area of Sannisegetusa Regia.

Like the rectangular Temples.118 The exterior circle of the Great Round Temple as a part of this monument

and (presumed) astronomical and mathematical tool.119 Some authors consider that this monument, even by the fact that it is

circular, must have calendar and astronomic functions.120 Expresis Verbis.121 Or, more exactly, a number to which only scarcely, and somewhat

artificially, we may assign an astronomical meaning.122 Some authors consider that this monument, even by the fact that it is

circular, must have calendar and astronomic functions.123 Our work is based on this description. See [DAICOVICIU, 1981, p.

235].124 In the first volume of the History of Rumanians, written by Constantin

C. Giurescu, published by the Academic Press, Bucharest, for the use of specialistsand of large public.

125 A polished stone founded in a Sacred Area of Sarmisegetusa City, nearthe Great Sanctuary.

126 Which seems very likely, taking in view that the Dacian-Getianhorseshoe enclosure is oriented at an angle differing by N = 50° from its Celtichomologous of Stonehenge.

127 Three intervals of the night, and three for the lighting day.This author is a forerunner of our own ideas.

128 Hypothesis without astronomical support.129 See the Proceedings of the respective session.130 For instance their equal size.


131 The existence to Dacians-Getians scientists the concept andrepresentation of the ellipse, as a definite geometrical object, or the existence, intheir science, of the Pythagorean rule for a rectangular triangle 92 + 122 152,

a.s.o. See [SOFONEA-IONESCU, 1993, p. 36].The number N = 72 may be obtained by labelling not only the 68

oaken/thin pillars, but equally the N = 4 stone thresholds.The claim that the Great Circular Sanctuary would include the

Pythagorean triangle 9 2 + 122 = 152 , gave rise to another problem: that of aDacian-Getian unit of length. Actually, what is really claimed is that the ratio ofthe radii of the two circles of the Great Sanctuary is N = 12/9 = 1.333. However,this is not supported by the topometric measurements N = 14 m / 10 m = 1.400.The difference between the two ratios is statistically significant. To save thesituation I. Rodean specified that both the radius of the great circle (made up of 30large/stone pillars), namely 14.01 m and the radius of the smaller circle (made upof 68 wooden pillars) namely N = 10.00 m refer to the inner sides of the circles,while the Pythagorean triangle would be constructed using the inner radius of thegreat circle and the outer radius of the smaller circle. According to his calculation,the thickness of the smaller circle is N = 0.40 m and, in addition, the value N =10.00 m should be corrected by N = 0.107 m (!). Finally, the two quantitiesadequately prepared would be N = 14.010 m and N = 10.507 m. Their ratio.is now N= 1.3334. We make no comment about the likelihood of such procedures. In itsturn, the existence of the Pythagorean triangle (claimed above) entitled the authorto derive the,Dacian unit of length N = 14.010/12 = 1.1675 m.

It is stated that the ancient Dacians-Getians were aware of the period ofequinoctium precession: just the modern value of T = 25920 years.

Equally fantastic are the opinion of other authors that the same Daciansestimated for the transcendent number n the value N = 3.1416, and determined(accurately!) the Earth-Sun distance and the Earth radius.

132 Speaking in the framework of a round-table.133 An equivalence between this new ring and the Aubrey's holes of

Stonehenge is not excluded. If this will be proved to be the case then theStonehenge-Sarmisegetusa analogy, upon which our scheme is devised, will bestill strengthened.

134 For instance, it is claimed that the diameter of the Earth divided by N =432000 and again divided by N = 17 (a number to be found in the structure of theGreat Temple) leads to the length unit used by Dacians, namely N = 1.734 m.

The results of this research being protected by a patent we cannot givemore details.

The problem/topics of the knowledge of an (relatively) exact value ofthe diameter of the Earth in Antiquity is, in fact, a complex problem/topics; itsmain aspects are: the reputed adequate method of Eratostene, the univocaldetermination of the unity employed, the plausible conjecture of different otherpossible, but unmentioned, attempts, et al.

135 After the calculations of C.A. Newham (from the paper "TheAstronomical Significations of Stonehenge", Moon Publications, 1972).

136 See [GLODARIU, IAROSLAVSKI, RUSU, 1989].


137 As it results from the presentation made by Pierre Kohler in Science etVie, nov. 1981.

138 Bisextil year.139 The firs topometric measurements did not find a local magnetic

anomaly.The sanctuaries are built within the space of an artificial terrace escaved

in a mountain with big slopes.140 Jean-Honoré Abdolonyme Ubicini (1987) Les origines de l'histoire

roumaine. Paris, Ernest Leroux, p. 36. Apud Hellanicus: tarrots xotteSele

rEtaiS.

141 Jean-Honoré Abdolonyme Ubicini (1987) Les origines de l'histoireroumaine. Paris, Ernest Leroux, p. 36. Apud Hellanicus: TeXetocs XOCTE3E4E

reMiS.

It is mentioned by Gr. Tocilesco, in 1880, in his study La Dacie avantles Romans.

142 Put forward much before the investigation of the Dacian-Getian calendar.143 See, for example, the research and the arguments of Al. Glodariu et al.,

exposed in their book "Cetáli i apezári dacice în Muntii Orásiei. Ghid al MunplorCoráltiei", Ed. Sport-Turism, Bucuresti. 1989; and those of H. Crisan exposed in"Spiritualitatea Geto-Dacica. Repere istorice". Ed. Albatros, Bucuresti, 1986.

144 See, for example, the research and the arguments of Al. Glodariu et al.,exposed in their book a§ezári dacice tn Muntii OrAstiei. Ghid al Muntilor

Bucuresti, Ed. Sport-Turism, 1989; and those of H. Crisan exposed inSpiritualitatea Geto-Dacica. Repere istorice. Bucuresti, Ed. Albatros, 1986.

145 By objects like: nails, needles, lamps, torches, a.s.

REFERENCES

BOBANCE, S., SAMOILA, C., POEÑARU, E. (1978) Calendarul de laSarmisegetusa Regia. Bucuresi, Editura Academiei.

DAICOVICIU, H. (1981) Dacia de la Burebista la cucerirea romata. Cluj-Napoca, Editura Dacia.

ELIADE, M. (1968) Traité d'Histoire des Religions. Paris, Payot.GEORGESCU, V. (1984) Istoria Románilor de la origini pán?; in zilele

nostre. A.R.A., American Romanian Academy of Arts and Sciences, Munich, IonDumitru Verlag.

GIURESCU, C.C. (1939-42) Istoria Románilor. Bucure§ti, Fundayio pentruLiteratur i Art5 Regele Carol al II-lea, 4 volumes.

GIURESCU, D.C. (1981) Illustrated history of the Romanian People.Bucurepti, Editura Sport-Turism.

GLODARIU, A., IAROSLAVSKI, E., RUSU, A. (1989) Cetaji airezdridacice in Munlii Orástiei, Ghid al Munplor Orásjiei. Bucuresi, Editura Sport-Turism.

HAWKINS, G.S. (1970) Stonehenge decoded. London, Fontane Collins.


HOYLE, F. (1972) From Stonehenge to Modern Cosmology. SanFrancisco, W.H. Freeman & Co.

IONESCU-PALLAS, N., SOFONEA, L. (1987) "A plausible model of theDacian calendar". Topics in Astrophysics, Astronomy and Space Sciences,3, 80-94.

RAO, N.K. (1993) "Astronomical orientation of the megalithic stomecircles of Brahmagiri Mysore state". Bull. Astr. Soc. India, 67-77.

SOFONEA, N., IONESCU-PALLAS, N. (1993) "Rechearches in PaleoAstronomy in Romania". In: Proceedings of the IIIrd National Conference onGeneral Relativity and Gravitation. Bistrip, Romania, 7-40.

SOFONEA, L., IONESCU-PALLAS, N. (1985) "Reconstructionsmathématiques de la paleoastronomie sur le teritoire de la Roumanie". In:Proceedings du Vifi me Congrés des Mathematiciens d'expression latine. Coimbra,365-370.

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